I am considering doing research in mathematics to be my career (and my life) someday.
I'm a visually oriented person in general , for example i prefer chess over cards because when i play chess i do all my thinking by looking at the board and analyzing it but when i play cards i have to remember things and calculate things because the details are not visible or visual, that's why i was doing very well with traditional plane geometry problems at school.
I was good at problems that can be visually explained or visually modeled . like proving the equality of two line segments or two angles just by looking at the figure . it has always been more interesting for me than Algebra where i had to write down terms and rearrange them to reach the solution .
now i am wondering if there is a branch in modern advanced mathematics that works the same way to be my research interest.
i am looking for kind of problems that i can call "visual puzzles" . problems that can be solved by looking at them
Is there such a field in modern mathematics that i can do research in ?
i realize the importance of algebra and mathematical logic . and i know that i must to use them , and i like to use them .
I am considering discrete geometry , but i am not sure if its problems are really visual
i have been looking for the advanced branches in geometry in the universities research pages . and i downloaded many research papers and books just to look at the advanced fields of geometry from inside and see how it "looks" like . i didn't understand anything for sure :-) i found topics like Non-euclidean geometry , differential geometry , topology , Riemann geometry ...etc
What really disappointed me is that i couldn't find a lot of figures !
I need your help to find the most interesting field for me